50 lines
1.6 KiB
Markdown
Executable File
50 lines
1.6 KiB
Markdown
Executable File
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# Game ideas
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- Math dominos:
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- Each problem is a domino tile, by difficulty.
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- Score is sum if 1st try, max if 2nd try. Subtract min if no solution.
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- Each team can have 2-3 dominos at a time. No free swaps.
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- Pick up dominos without knowing problem.
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- что-где-когда:
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- All teams solve one problem at once.
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- Spacewar!:
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- Two teams, each starts in one root node.
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- Graph of problems, symmetric across middle
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- easy problems close, hard problems far.
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- Goal: capture as many nodes as possible
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- Solve a problem, capture a node
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- solve a problem on the other team's side, capture their node.
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- TODO: a fun way to resolve conflicts?
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# Topics:
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- Divisibility proofs & properties
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- 1 exists ==> assume 2 exist
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- <= , >= ==> =
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- pidgeonhole
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# Handout ideas:
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- Notation toolbox
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- Propositional logic
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- Rubik's group
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- Graph combinatorics
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- Fourier transforms
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- Probabilistic proofs
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- Bayesian / Frequentist probability
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- Data structures
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# Handouts to clean up:
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- Euler's number
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- Lattices
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- Nim handout
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- Stocks
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# Problems to record:
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- Nikita: weight of 100 cows
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- Seat swapping: everyone wants a seat that's not their own, no two people want the same seat. Each cycle, everyone swaps. Min # of cycles? Solution: 2, reflect. use even and odd cycles. Takeaway: composition of reflections is rotation.
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- Geometric optimization: ant on cube shortest path, ant on brick shortest path, ribbon on brick (over-under, h-shape) minimal length, Farthest point from corner of brick
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- 180: Sperner lemma and brouwer theorem
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- 25 horses. 5 at a time. find top 3? (7 races)
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